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The value of `lambda` for which the curve `(7x + 5)^2 + (7y + 3)^2 = lambda^2 (4x + 3y-24)^2` represents a parabola isA. `+-(6)/(5)`B. `+-(7)/(5)`C. `+-(1)/(5)`D. `+-(2)/(5)` |
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Answer» Correct Answer - B Given curve is `(7x+5)^2+(7y+3)^2` `=lambda^2(4x+3y-24y)^2` `rArr 49x^2+25+70x+49y^2+9+42y` `lambda^2(16x^2+9y^2+576+24xy-144y-192x)` `rArr (49-16lambda^2)x^2+(39-9lambda^2)y^2+(70+192lambda^2)x+(42+144lambda^2)y-24lambda^2xy+(25-576lambda^2)=0` On comparing with `ax^2+2hxy+by^2+2gh+2fy+c=0` we get `a=49-16lambda^2,b=(49-9lambda^2)` `h=-12lambda^2` Condition for parabola is `ab=h^2` `therefore (49-16lambda^2)(49-9lambda^2)=(-12lambda^2)^2` `rArr 2401-441lambda^2-784lambda^2+144lambda^4-144lambda^4=0` `rArr 2401-1225lambda^2=0` `rArr lambda^2=(2401)/(1225)rArr lambda^2=((49)^2)/((35)^2)` `rArr lambda=+-(49)/(35)` `therefore lambda=+-(7)/(5)` |
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